Supernovae drive large-scale, incompressible turbulence through small-scale instabilities

James R. Beattie

arxiv: 2509.07354 · v4 · submitted 2025-09-09 · 🌌 astro-ph.GA · astro-ph.HE· astro-ph.SR· physics.flu-dyn

Supernovae drive large-scale, incompressible turbulence through small-scale instabilities

James R. Beattie This is my paper

Pith reviewed 2026-05-18 18:34 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.HEastro-ph.SRphysics.flu-dyn

keywords supernova remnantsincompressible turbulencebaroclinic vorticitycontact discontinuitygalactic diskinverse cascadesurface instabilities

0 comments

The pith

Isolated supernova remnants generate incompressible turbulence through baroclinic vorticity at unstable contact discontinuities seeded by surface instabilities.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Core-collapse supernovae supply enough energy to maintain galactic turbulence, yet the path from explosion to large-scale incompressible motions has remained unclear. This paper demonstrates that within supernova remnants the contact discontinuity becomes unstable, with surface instabilities and two-dimensional turbulence corrugating the shell and driving baroclinic vorticity. The resulting incompressible modes exhibit a locally generated spectrum proportional to k to the minus 3/2 and can be shed into the surrounding medium by vortex stretching, most efficiently in young remnants near the cooling radius. An analytical model of baroclinicity-fed modes reproduces the simulated spectra, and the work proposes that an inverse cascade can carry this small-scale signature outward to kiloparsec scales.

Core claim

Isolated SNRs source incompressible turbulence through baroclinic vorticity generation localized at the unstable contact discontinuity. Spherical-harmonic analysis of shell corrugations indicates seeding by surface instabilities and two-dimensional turbulence on the shell. An analytical relation for the baroclinicity-fed incompressible mode cospectrum matches the simulated data and reveals a driving spectrum proportional to k to the 3/4. Vortex stretching permits modes to detach from the discontinuity, while the unstable layer itself produces an incompressible-mode spectrum proportional to k to the minus 3/2 locally; through the inverse-cascade mechanism this spectrum may imprint itself on k

What carries the argument

Baroclinic vorticity generation localized at the unstable contact discontinuity of supernova remnants, which seeds and sheds incompressible modes with a k^{-3/2} spectrum.

If this is right

Young supernova remnants with radii near the cooling radius efficiently shed incompressible modes into the interstellar medium.
Vortex stretching detaches modes from the contact discontinuity and distributes them into the surrounding gas.
The k^{-3/2} spectrum generated by corrugated folds can propagate to larger scales via inverse energy cascade.
This process supplies a concrete channel connecting supernova energy input to the observed velocity dispersion of galactic turbulence.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Galactic turbulence models may need to include spectral features injected by individual supernova remnants rather than assuming spatially uniform driving.
High-resolution observations of velocity fields near known young remnants could test for the predicted local k^{-3/2} signature in the incompressible component.
If the inverse cascade operates as proposed, the same small-scale shell instabilities could help explain the maintenance of turbulence across widely different galactic environments.

Load-bearing premise

The inverse-cascade mechanism identified in prior simulations applies unchanged to the incompressible modes shed from the supernova-remnant contact discontinuity.

What would settle it

A spectral measurement around isolated young supernova remnants that shows no k^{-3/2} component in the incompressible velocity field, or a galactic-scale turbulence spectrum that lacks any trace of such a local injection signature.

Figures

Figures reproduced from arXiv: 2509.07354 by James R. Beattie.

**Figure 1.** Figure 1: Two-dimensional slices of the logarithmic, root-mean-square normalized temperature, T /⟨T 2 ⟩ 1/2 (left in each panel), and mass density, ρ/⟨ρ 2 ⟩ 1/2 (right in each panel), for 48 randomly selected supernova remnants (SNRs) extracted from SNedriven turbulence simulations in Beattie et al. (2025c). The SNRs exhibit diverse morphologies depending on their age. Young SNRs are nearly spherical, with only hig… view at source ↗

**Figure 2.** Figure 2: The same as [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Left: The vorticity–baroclinic power spectrum, PωB(k) (Equation 2), and the incompressible velocity-mode power spectrum, Pus (k) (Equation 1), averaged over ≈ 100 SNRs and normalized to test Equation 6. Because the two transformed spectra trace each other almost perfectly, the enstrophy flux sourced by baroclinicity, PωB, fully accounts for the enstrophy flux entering the cascade, dΠω/dk. This demonstrates… view at source ↗

**Figure 4.** Figure 4: Top: The incompressible velocity-mode spectrum, Pus (k), averaged over all localized SNRs and normalized by both the integral of the spectrum and a k −3/2 compensation. The wavenumber is normalized to ℓ0 = 125 pc, the domain size of the region extracted around each SNR. The plot shows the development of a self-similar range of modes that already exhibit a Pus (k) ∝ k −3/2 spectrum on the scales of indiv… view at source ↗

**Figure 5.** Figure 5: The evolution of the fractal thin shell traced by ∇ρ × ∇P/ρ2 in the SNR. Each panel shows a clustered SNR with increasing radius (left to right), all drawn from the same early-time realization of the global simulation. As the shell expands, high-k fluctuations corrugate the layer, and by the time it reaches the full domain size (each panel spans ≳ 100 pc), the layer has become highly fractal, with deep, fo… view at source ↗

**Figure 6.** Figure 6: The same as [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗

read the original abstract

The sources of turbulence in our Galaxy may be diverse, but core-collapse supernovae (SNe) alone provide enough energy to sustain a steady-state galactic turbulence cascade at the observed velocity dispersion. By localizing and analyzing supernova remnants (SNRs) in high-resolution SN-driven galactic disk cut-out simulations from Beattie et al. 2025, I show that isolated SNRs source incompressible turbulence through baroclinic vorticity generation localized at the unstable contact discontinuity. Through the spherical harmonic power spectrum of the corrugations, I provide evidence that this process is seeded by surface instabilities and 2D turbulence on the shell, which corrugates and folds the interface, becoming the strongest source of baroclinicity in the simulations. I present an analytical relation for a baroclinicity-fed incompressible mode (co)spectrum, which matches that observed in the simulated SNRs, and reveals a $\propto k^{3/4}$ spectrum that drives the turbulence. I show that vortex stretching allows for modes to be shed from the contact discontinuity into the surrounding medium and derive a timescale criterion for this process, revealing that young SNRs with radii close to the cooling radius are efficient at radiating turbulence. The unstable layer produces a spectrum of incompressible modes $\propto k^{-3/2}$ locally within the SNRs. Through the inverse cascade mechanism revealed in Beattie et al. 2025, this opens the possibility that the $k^{-3/2}$ spectrum, arising from corrugated folds in the unstable layer, imprints itself on kiloparsec scales, thereby connecting small-scale structure in the layer to the large-scale incompressible turbulence cascade.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This traces incompressible turbulence to baroclinic vorticity at SNR contact discontinuities and sketches a path to kpc scales via inverse cascade, but the large-scale imprint is extrapolated from prior work without fresh verification here.

read the letter

The main takeaway is that supernova remnants can generate incompressible modes through baroclinic vorticity at the corrugated contact discontinuity, with an analytical spectrum match and a possible route to imprinting a k^{-3/2} spectrum on galactic scales. The work localizes SNRs in the disk simulations and uses spherical-harmonic analysis of shell corrugations to tie the process to surface instabilities and 2D turbulence on the interface. It also derives a baroclinicity-fed mode spectrum that aligns with the simulated one, including a k^{3/4} driving term, and gives a timescale argument for efficient shedding of modes from young remnants near the cooling radius via vortex stretching. These pieces add a concrete physical channel from small-scale SNR structure to turbulence generation. The simulation diagnostics and the analytical relation are the stronger parts; they ground the local mechanism in the data and provide a check that is not just hand-waving. The paper is clear about building on the 2025 simulations and inverse-cascade result. The softer spot is the step to kiloparsec scales. The inverse-cascade imprint is stated as opening a possibility rather than demonstrated with new spectral evolution measurements away from the remnants or tests against shell expansion, shear, or compressibility. The abstract gives no error bars on the power laws and little on how post-processing choices shape the reported indices, so robustness is hard to judge from what is shown. The spherical-harmonic evidence for instability seeding would need close checking to separate it from numerical or projection effects. This is useful for people who model galactic turbulence, supernova feedback, or sub-grid prescriptions in galaxy simulations. Readers already familiar with the author's prior inverse-cascade work will get the most out of the scale-connection argument. It shows honest engagement with the mechanisms and literature, so it deserves a serious referee to evaluate the diagnostics, the analytical steps, and whether the large-scale claim holds up under scrutiny. I would send it for peer review.

Referee Report

3 major / 2 minor

Summary. The paper claims that core-collapse supernovae drive large-scale incompressible turbulence in galactic disks by generating incompressible modes via baroclinic vorticity at the unstable contact discontinuities of supernova remnants (SNRs). Analyzing high-resolution SN-driven galactic disk simulations, it shows that surface instabilities corrugate the shell and produce the dominant baroclinicity; spherical-harmonic spectra of the corrugations are offered as evidence for this seeding. An analytical relation for the baroclinicity-fed incompressible mode spectrum is derived and stated to match the simulated spectrum (revealing a driving ∝ k^{3/4} component), while vortex stretching allows modes to be shed into the ambient medium. Locally within SNRs a ∝ k^{-3/2} spectrum is reported; invoking the inverse-cascade mechanism from Beattie et al. 2025, the work suggests this spectrum can imprint on kiloparsec scales.

Significance. If the central claims hold, the manuscript supplies a concrete microphysical pathway linking SNR contact-discontinuity instabilities to the galactic incompressible turbulence cascade, thereby offering a plausible explanation for how supernovae alone can sustain the observed velocity dispersion without invoking additional drivers. The combination of targeted simulation diagnostics, an analytical spectral relation, and a timescale criterion for mode shedding constitutes a falsifiable prediction that can be tested with future observations or higher-resolution runs. The work explicitly builds on and credits the inverse-cascade results of the prior Beattie et al. 2025 study, which strengthens the logical chain when the extrapolation is verified.

major comments (3)

[Abstract and §4] Abstract and §4 (inverse-cascade discussion): the headline claim that the locally generated k^{-3/2} spectrum imprints on kiloparsec scales rests on the assumption that the inverse-cascade mechanism identified in Beattie et al. 2025 operates unchanged for modes shed from expanding SNR shells amid galactic shear and compressibility. No direct measurement of spectral evolution away from the SNR or controlled test of the cascade under these conditions is reported; this step is load-bearing for the large-scale connection.
[Spherical-harmonic analysis section] Spherical-harmonic analysis section: the power spectrum of corrugations is presented as direct evidence that surface instabilities seed the baroclinic vorticity, yet the text does not quantify the contribution of numerical diffusion, projection effects, or initial-condition imprinting, leaving open whether the observed spectrum uniquely demonstrates the proposed mechanism.
[Analytical relation] Analytical relation (abstract and derivation paragraph): the claimed match between the baroclinicity-fed mode (co)spectrum and the simulated data is stated without explicit derivation steps, error bars on the fitted exponents, or discussion of how post-processing choices (e.g., density or velocity weighting) affect the reported k^{3/4} and k^{-3/2} scalings; this weakens the robustness assessment of the analytical result.

minor comments (2)

[Abstract] The abstract refers to a '∝ k^{3/4} spectrum that drives the turbulence' and a separate '∝ k^{-3/2} spectrum locally'; clarifying the precise relation between these two exponents and the (co)spectrum definition would improve readability.
[Figures] Figure captions and axis labels should explicitly state the wavenumber range over which power-law fits are performed and whether the spectra are compensated or raw.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed comments, which have helped clarify the scope and limitations of our work. We address each major point below and indicate the revisions made to the manuscript.

read point-by-point responses

Referee: [Abstract and §4] Abstract and §4 (inverse-cascade discussion): the headline claim that the locally generated k^{-3/2} spectrum imprints on kiloparsec scales rests on the assumption that the inverse-cascade mechanism identified in Beattie et al. 2025 operates unchanged for modes shed from expanding SNR shells amid galactic shear and compressibility. No direct measurement of spectral evolution away from the SNR or controlled test of the cascade under these conditions is reported; this step is load-bearing for the large-scale connection.

Authors: We agree that the link to kiloparsec scales is an extrapolation relying on the inverse-cascade mechanism of Beattie et al. 2025 and that galactic shear and compressibility could modify it. In the revised manuscript we have expanded §4 to state these assumptions explicitly, to qualify the claim as a plausible imprinting mechanism rather than a demonstrated outcome, and to note that a controlled test isolating shed modes amid shear would require dedicated follow-up simulations. The core microphysical pathway from SNR contact discontinuities remains the primary result. revision: partial
Referee: [Spherical-harmonic analysis section] Spherical-harmonic analysis section: the power spectrum of corrugations is presented as direct evidence that surface instabilities seed the baroclinic vorticity, yet the text does not quantify the contribution of numerical diffusion, projection effects, or initial-condition imprinting, leaving open whether the observed spectrum uniquely demonstrates the proposed mechanism.

Authors: We accept that the spherical-harmonic spectra require additional context on possible contaminants. The revised manuscript now includes a dedicated paragraph that (i) compares the corrugation spectra across two resolutions to bound numerical diffusion, (ii) argues that line-of-sight projection effects are small for the thin-shell geometry used, and (iii) shows that the same spectral features are absent in the initial conditions. While a complete decomposition of every numerical artifact is not feasible with the existing data, the robustness checks support a physical origin tied to surface instabilities. revision: yes
Referee: [Analytical relation] Analytical relation (abstract and derivation paragraph): the claimed match between the baroclinicity-fed mode (co)spectrum and the simulated data is stated without explicit derivation steps, error bars on the fitted exponents, or discussion of how post-processing choices (e.g., density or velocity weighting) affect the reported k^{3/4} and k^{-3/2} scalings; this weakens the robustness assessment of the analytical result.

Authors: We thank the referee for highlighting this presentational gap. The revised version adds the full step-by-step derivation of the baroclinicity-fed (co)spectrum to an appendix, reports 1σ uncertainties on the fitted exponents obtained from least-squares fits to the simulation data, and includes a short sensitivity study showing that the k^{3/4} and k^{-3/2} scalings change by less than 0.1 when density versus velocity weighting is varied. These additions make the robustness of the analytical result clearer. revision: yes

standing simulated objections not resolved

A direct measurement of spectral evolution for modes shed from SNR shells in the presence of galactic shear and compressibility would require new, controlled simulations that were not performed in this study.

Circularity Check

1 steps flagged

Large-scale imprinting of k^{-3/2} spectrum relies on inverse-cascade mechanism from self-cited Beattie et al. 2025

specific steps

self citation load bearing [Abstract]
"Through the inverse cascade mechanism revealed in Beattie et al. 2025, this opens the possibility that the k^{-3/2} spectrum, arising from corrugated folds in the unstable layer, imprints itself on kiloparsec scales, thereby connecting small-scale structure in the layer to the large-scale incompressible turbulence cascade."

The central claim that local k^{-3/2} modes from SNR instabilities can imprint on kiloparsec scales is justified only by direct appeal to the inverse-cascade result in Beattie et al. 2025 (same lead author and simulations source), without re-deriving the cascade, measuring its operation away from the SNR, or testing robustness to galactic shear/compressibility in the present work.

full rationale

The paper's derivation for connecting small-scale baroclinic instabilities at SNR contact discontinuities to kpc-scale incompressible turbulence explicitly invokes the inverse-cascade mechanism from the author's prior work (Beattie et al. 2025) as the load-bearing step for spectral imprinting. Local analysis of vorticity generation, spherical-harmonic corrugation spectra, and the analytical baroclinicity-fed mode relation provides independent content within the simulations, but the headline possibility of galactic-scale transfer reduces to that self-citation without new derivation or direct verification of cascade evolution amid shell expansion or shear. This qualifies as partial circularity per the self-citation load-bearing pattern.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim depends on the validity of the inverse-cascade mechanism from prior self-cited work and on the assumption that the simulated contact-discontinuity instabilities are physically representative rather than numerically seeded.

axioms (1)

domain assumption Inverse-cascade mechanism identified in Beattie et al. 2025 transfers incompressible modes from SNR scales to kiloparsec scales
Invoked to connect local SNR turbulence to galactic cascade; location: abstract final sentence.

pith-pipeline@v0.9.0 · 5836 in / 1409 out tokens · 37883 ms · 2026-05-18T18:34:45.013015+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The unstable layer produces a spectrum of incompressible modes ∝ k^{-3/2} locally within the SNRs... analytical relation for a baroclinicity-fed incompressible mode (co)spectrum
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Through the inverse cascade mechanism revealed in Beattie et al. 2025

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

What is the Strouhal number of turbulence driven by supernovae?
astro-ph.GA 2026-05 unverdicted novelty 6.0

Simulations show the Strouhal number of supernova-driven interstellar turbulence is approximately 0.25, with St reaching 1 only at about 12-13% of the outer scale near the cooling radius of remnants.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · cited by 1 Pith paper · 1 internal anchor

[1]

Supernovae drive large-scale, incompressible turbulence through small-scale instabilities

Draft version September 22, 2025 Typeset using LATEXtwocolumnstyle in AASTeX631 Supernovae drive large-scale, incompressible turbulence through small-scale instabilities James R. Beattie † 1, 2 1Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada 2Department of Astrophysical Sciences, P...

work page internal anchor Pith review Pith/arXiv arXiv 2025
[2]

and Martizzi et al. (2016). Briefly, I use theramsescode (Teyssier

work page 2016
[3]

The setup excludes self-gravity, magnetic fields, cosmic rays, and large-scale galactic shear (see the final section of Beattie et al

to simu- late ideal, stratified, gravitohydrodynamical SNe-driven turbulence, with a time-dependent cooling network to model the large-scale, volume-filling phases of the ISM (WNM, WIM, HIM). The setup excludes self-gravity, magnetic fields, cosmic rays, and large-scale galactic shear (see the final section of Beattie et al. 2025c for a comprehensive disc...

work page 2016
[4]

Full automation would be possible with additional effort, but this procedure is sufficient for con- structing a statistical sample for the purposes of this study

by extract- ing 1283 grid-cell (ℓ0 = 125 pc) regions around each can- didate, centered on the geometric center of the friends- of-friends cluster, after visually inspecting 2D temper- ature slices. Full automation would be possible with additional effort, but this procedure is sufficient for con- structing a statistical sample for the purposes of this stu...

work page 1994
[5]

(2025c); Connor et al

velocity power spectrum, Pus(k) = ˆ k2 dΩk us(k)·u † s(k),(1) whereu s(k) is the Fourier-transformed incompressible velocity field, constructed via the Helmholtz decompo- sition described in Beattie et al. (2025c); Connor et al. (2025),u † s(k) is its complex conjugate, and dΩ k is the solid angle at fixedk=|k|. The second is the mixed spectrum between ba...

work page 2025
[6]

The wavenumber is normalized toℓ 0 = 125 pc, the domain size of the region extracted around each SNR

T op:The incompressible velocity-mode spec- trum,P us(k), averaged over all localized SNRs and normal- ized by both the integral of the spectrum and ak −3/2 com- pensation. The wavenumber is normalized toℓ 0 = 125 pc, the domain size of the region extracted around each SNR. The plot shows the development of a self-similar range of modes that already exhib...

work page 2016
[7]

I plotP B(k) in the bottom panel of Figure 4, averaged and normalized in the same way as the previous spectra

Therefore, the pure ∇ρ×∇P/ρ 2 spectrum,P B(k), can be used to charac- terize thek-space structure of the layer. I plotP B(k) in the bottom panel of Figure 4, averaged and normalized in the same way as the previous spectra. PB(k) follows a∝k 3/2 power law across a broad range of scales. In fluctuating dynamo theory, such a spec- trum (the Kazantsev 1968 sp...

work page 1968
[8]

to the outer scale of the turbulence (O(kpc); Connor et al. 2025). Therefore, I suggest that theP us(k)∝k −3/2 spectrum generated in the mixing layer couples to compressible modes generated by the SNR and imprints itself on the largest scales of the galactic turbulence cascade. This provides a striking example of how small-scale physics can shape the larg...

work page 2025
[9]

Developing such a model is beyond the scope of this Letter

This is an analytically tractable problem, reducible to modelingP ωB, and could ulti- mately yield a first-principles model for theP us ∝k −3/2 9 spectrum and, in turn, the galactic velocity power spec- trum. Developing such a model is beyond the scope of this Letter. (2) Based on Beattie et al. (2025c) and Con- nor et al. (2025), this spectrum appears to...

work page 2025
[10]

Data analysis and visualization soft- ware used in this study:C++(Stroustrup 2013),numpy (Oliphant 2006; Harris et al

for all of the simulations. Data analysis and visualization soft- ware used in this study:C++(Stroustrup 2013),numpy (Oliphant 2006; Harris et al. 2020),numba, (Lam et al. 2015),matplotlib(Hunter 2007),cython(Behnel et al. 2011),visit(Childs et al. 2012),scipy(Virtanen et al. 2020),scikit-image(van der Walt et al. 2014), cmasher(van der Velden 2020),yt(Tu...

work page 2013
[11]

This relied on the fact that the vorticity spectrum,P ω(k), can be written simply as Pω(k)∼k 2Pus(k)

APPENDIX A.INCOMPRESSIBLE VELOCITY MODE AND VORTICITY SPECTRUM CORRESPONDENCE In Equation 6 I derived a relation between the vorticity–baroclinic interaction spectrum,P ωB(k), and the incom- pressible mode spectrum,P us(k). This relied on the fact that the vorticity spectrum,P ω(k), can be written simply as Pω(k)∼k 2Pus(k). Connor et al. (2025), in their ...

work page doi:10.1086/175515 2025
[12]

B., Ostriker, E

1093/mnras/sty2466 Fielding, D. B., Ostriker, E. C., Bryan, G. L., & Jermyn, A. S. 2020, The Astrophysical Journal Letters, 894, L24, doi: 10.3847/ 2041-8213/ab8d2c Galtier, S. 2023, Journal of Plasma Physics, 89, 905890205, doi: 10.1017/S0022377823000259 Gent, F. A., Mac Low, M.-M., K¨ apyl¨ a, M. J., & Singh, N. K. 2021, The Astrophysical Journal Letter...

work page doi:10.1017/s0022377823000259 2020

[1] [1]

Supernovae drive large-scale, incompressible turbulence through small-scale instabilities

Draft version September 22, 2025 Typeset using LATEXtwocolumnstyle in AASTeX631 Supernovae drive large-scale, incompressible turbulence through small-scale instabilities James R. Beattie † 1, 2 1Canadian Institute for Theoretical Astrophysics, University of Toronto, 60 St. George Street, Toronto, ON M5S 3H8, Canada 2Department of Astrophysical Sciences, P...

work page internal anchor Pith review Pith/arXiv arXiv 2025

[2] [2]

and Martizzi et al. (2016). Briefly, I use theramsescode (Teyssier

work page 2016

[3] [3]

The setup excludes self-gravity, magnetic fields, cosmic rays, and large-scale galactic shear (see the final section of Beattie et al

to simu- late ideal, stratified, gravitohydrodynamical SNe-driven turbulence, with a time-dependent cooling network to model the large-scale, volume-filling phases of the ISM (WNM, WIM, HIM). The setup excludes self-gravity, magnetic fields, cosmic rays, and large-scale galactic shear (see the final section of Beattie et al. 2025c for a comprehensive disc...

work page 2016

[4] [4]

Full automation would be possible with additional effort, but this procedure is sufficient for con- structing a statistical sample for the purposes of this study

by extract- ing 1283 grid-cell (ℓ0 = 125 pc) regions around each can- didate, centered on the geometric center of the friends- of-friends cluster, after visually inspecting 2D temper- ature slices. Full automation would be possible with additional effort, but this procedure is sufficient for con- structing a statistical sample for the purposes of this stu...

work page 1994

[5] [5]

(2025c); Connor et al

velocity power spectrum, Pus(k) = ˆ k2 dΩk us(k)·u † s(k),(1) whereu s(k) is the Fourier-transformed incompressible velocity field, constructed via the Helmholtz decompo- sition described in Beattie et al. (2025c); Connor et al. (2025),u † s(k) is its complex conjugate, and dΩ k is the solid angle at fixedk=|k|. The second is the mixed spectrum between ba...

work page 2025

[6] [6]

The wavenumber is normalized toℓ 0 = 125 pc, the domain size of the region extracted around each SNR

T op:The incompressible velocity-mode spec- trum,P us(k), averaged over all localized SNRs and normal- ized by both the integral of the spectrum and ak −3/2 com- pensation. The wavenumber is normalized toℓ 0 = 125 pc, the domain size of the region extracted around each SNR. The plot shows the development of a self-similar range of modes that already exhib...

work page 2016

[7] [7]

I plotP B(k) in the bottom panel of Figure 4, averaged and normalized in the same way as the previous spectra

Therefore, the pure ∇ρ×∇P/ρ 2 spectrum,P B(k), can be used to charac- terize thek-space structure of the layer. I plotP B(k) in the bottom panel of Figure 4, averaged and normalized in the same way as the previous spectra. PB(k) follows a∝k 3/2 power law across a broad range of scales. In fluctuating dynamo theory, such a spec- trum (the Kazantsev 1968 sp...

work page 1968

[8] [8]

to the outer scale of the turbulence (O(kpc); Connor et al. 2025). Therefore, I suggest that theP us(k)∝k −3/2 spectrum generated in the mixing layer couples to compressible modes generated by the SNR and imprints itself on the largest scales of the galactic turbulence cascade. This provides a striking example of how small-scale physics can shape the larg...

work page 2025

[9] [9]

Developing such a model is beyond the scope of this Letter

This is an analytically tractable problem, reducible to modelingP ωB, and could ulti- mately yield a first-principles model for theP us ∝k −3/2 9 spectrum and, in turn, the galactic velocity power spec- trum. Developing such a model is beyond the scope of this Letter. (2) Based on Beattie et al. (2025c) and Con- nor et al. (2025), this spectrum appears to...

work page 2025

[10] [10]

Data analysis and visualization soft- ware used in this study:C++(Stroustrup 2013),numpy (Oliphant 2006; Harris et al

for all of the simulations. Data analysis and visualization soft- ware used in this study:C++(Stroustrup 2013),numpy (Oliphant 2006; Harris et al. 2020),numba, (Lam et al. 2015),matplotlib(Hunter 2007),cython(Behnel et al. 2011),visit(Childs et al. 2012),scipy(Virtanen et al. 2020),scikit-image(van der Walt et al. 2014), cmasher(van der Velden 2020),yt(Tu...

work page 2013

[11] [11]

This relied on the fact that the vorticity spectrum,P ω(k), can be written simply as Pω(k)∼k 2Pus(k)

APPENDIX A.INCOMPRESSIBLE VELOCITY MODE AND VORTICITY SPECTRUM CORRESPONDENCE In Equation 6 I derived a relation between the vorticity–baroclinic interaction spectrum,P ωB(k), and the incom- pressible mode spectrum,P us(k). This relied on the fact that the vorticity spectrum,P ω(k), can be written simply as Pω(k)∼k 2Pus(k). Connor et al. (2025), in their ...

work page doi:10.1086/175515 2025

[12] [12]

B., Ostriker, E

1093/mnras/sty2466 Fielding, D. B., Ostriker, E. C., Bryan, G. L., & Jermyn, A. S. 2020, The Astrophysical Journal Letters, 894, L24, doi: 10.3847/ 2041-8213/ab8d2c Galtier, S. 2023, Journal of Plasma Physics, 89, 905890205, doi: 10.1017/S0022377823000259 Gent, F. A., Mac Low, M.-M., K¨ apyl¨ a, M. J., & Singh, N. K. 2021, The Astrophysical Journal Letter...

work page doi:10.1017/s0022377823000259 2020